Mean, median and mode
Data
Definition
There are three traditional types of averages: mean, median and mode
The arithmetic mean of a list of numbers is the sum of the data values divided by the number of numbers in the list. In everyday language, the arithmetic mean is commonly called the average.
The median is the value in a set of ordered data that divides the data into two parts. It is frequently called the middle value.
The mode is the most frequently occurring value in a set of data. (NSW Mathematics K-10 syllabus)
The mean, median and mode are all valid descriptions of data and have different functions with specific kinds of data. (Siemon, et al, 2019)
Teaching and learning activities
The resources below provide targeted teaching strategies to support student improvement in this skill.
Each downloadable lesson activity includes:
learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials
Select the download all icon to download all available activities or select each activity separately.
PLAN2 Areas of focus
An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.
Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.
For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page.
Relevance to the numeracy test marking
The feedback for a Level 3 performance in the HSC minimum standard online numeracy test states:
Individuals performing at this level typically select appropriate strategies from a variety of everyday mathematical processes in familiar and some less familiar contexts. They interpret and comprehend mathematical information in written material, diagrams, charts and tables.
Students are able to use and apply simple measures of spread involving the mean, mode and median.
Connections with ACSF Level 3 descriptors
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how measures of spread are assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts
Focus area: Explicitness of mathematical information
Level 3 performance features:
interprets and comprehends a range of everyday mathematical information that is embedded in familiar and routine contexts
Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts
Focus area: Problem solving processes including estimating and reflecting
Level 3 performance features:
uses developing estimation, and other assessment skills, to check and reflect on the outcome and its appropriateness to the context and task
Focus area: Mathematical methods and use of tools
Level 3 performance features:
uses a blend of personal ‘in-the-head’ methods and formal pen and paper methods to calculate and uses calculator/technological processes and tools to undertake the problem solving process
Numeracy Indicator 3.11: Uses a combination of both informal and formal oral and written mathematical language and representation to communicate mathematically
Focus area: Oral mathematical language
Level 3 performance features:
uses a combination of both informal and formal oral mathematical and general language to present and discuss the mathematical and problem solving process and result
Connections with Numeracy Learning Progression:
The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to measures of spread are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.
Element: Statistics and probability
Sub-element: Interpreting and representing data (IRD)
IRD5 — Collecting, displaying continuous data
determines and calculates the most appropriate statistic to describe the spread of data
calculates simple descriptive statistics such as mode, mean or median as measures to represent typical values of a distribution